This paper presents the analytic investigation of the effect of noise on the Fidelity of Photonic Qubit based deterministic CNOT gate (designed employing quantum dot (QD) spin within the double sided optical micro-cavity), considering vacuum noise and sideband leakage. It is found that the performance of the CNOT gate is significantly dependent on the interaction between the spin of QD and photon within the optical cavity. In strong (g/k = 2.5 and k(s)/k = 0.05) and weak (g/k = 0.4 and k(s)/k = 1) coupling conditions the calculated fidelity is 57.14 and 56.23 respectively. The analysis demonstrates that the CNOT gate works satisfactorily in both high and weak coupling regime under noisy condition. The computed maximum fidelity for CNOT gate and compact CNOT gate model is 58.17 at (g/k = 4 and k(s)/k = 0.01 and 77.19 at (g/k = 0.1 and k(s)/k = 0.01 respectively under noisy conditions. The study can be used in the optimization of the performance of any quantum circuit, having a QD cavity system for photonic Qubits, under noisy conditions.
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